Deck 4: Estimating Demand

Question 1

Consider the following multiplicative demand function where Q_D = quantity demanded,P = selling price,and Y = disposable income: $$Q _ { D } = 1.6 \mathrm { P } ^ { - 15 } \mathrm { Y } ^ { 2 }$$ The coefficient of Y indicates that (all other things being held constant):

A) for a one percent increase in disposable income,quantity demanded would increase by .2 percent
B) for a one unit increase in disposable income,quantity demanded would increase by .2 units
C) for a one percent increase in disposable income quantity demanded would increase by .2 units
D) for a one unit increase in disposable income,quantity demanded would increase by .2 percent
E) none of the above

Answer 1

for a one percent increase in disposable income,quantity demanded would increase by .2 percent

Question 2

The Identification Problem in the development of a demand function is a result of:

A) the variance of the demand elasticity
B) the consistency of quantity demanded at any given point
C) the negative slope of the demand function
D) the simultaneous relationship between the demand and supply functions
E) none of the above

Answer 2

D

Question 3

Demand functions in the multiplicative form are most common for all of the following reasons except:

A) elasticities are constant over a range of data
B) ease of estimation of elasticities
C) exponents of parameters are the elasticities of those variables
D) marginal impact of a unit change in an individual variable is constant
E) c and d

Answer 3

D

Question 4

The principal econometric techniques used in measuring demand relationships are:

A) the standard deviation
B) regression
C) correlation analysis
D) the coefficient of determination
E) both b and c

Question 5

The coefficient of determination ranges in value between 0.0 and 1.0.

Question 6

The correlation coefficient ranges in value between 0.0 and 1.0.

Question 7

In regression analysis,the existence of a high degree of intercorrelation among some or all of the explanatory variables in the regression equation constitutes:

A) autocorrelation
B) a simultaneous equation relationship
C) nonlinearities
D) heteroscedasticity
E) multicollinearity

Question 8

A study of expenditures on food in cities resulting in the following equation: Log E = 0.693 Log Y + 0.224 Log N
Where E is Food Expenditures; Y is total expenditures on goods and services; and N is the size of the family.This evidence implies:

A) that as total expenditures on goods and services rises,food expenditures falls.
B) that a one-percent increase in family size increases food expenditures .693%.
C) that a one-percent increase in family size increases food expenditures .224%.
D) that a one-percent increase in total expenditures increases food expenditures 1%.
E) that as family size increases,food expenditures go down.

Question 9

The standard deviation of the error terms in an estimated regression equation is known as:

A) coefficient of determination
B) correlation coefficient
C) Durbin-Watson statistic
D) standard error of the estimate
E) none of the above

Question 10

Consider the following linear demand function where Q_D = quantity demanded,P = selling price,and Y = disposable income: Q_D = −36 −2.1P + .24Y
The coefficient of P indicates that (all other things being held constant):

A) for a one percent increase in price,quantity demanded would decline by 2.1 percent
B) for a one unit increase in price,quantity demanded would decline by 2.1 units
C) for a one percent increase in price,quantity demanded would decline by 2.1 units
D) for a one unit increase in price,quantity demanded would decline by 2.1 percent
E) none of the above

Question 11

One commonly used test in checking for the presence of autocorrelation when working with time series data is the ____.

A) F-test
B) Durbin-Watson test
C) t-test
D) z-test
E) none of the above

Question 12

When using a multiplicative power function (Y = a X₁^b1X₂^b2X₃^b3)to represent an economic relationship,estimates of the parameters (a,and the b's)using linear regression analysis can be obtained by first applying a ____ transformation to convert the function to a linear relationship.

A) semilogarithmic
B) double-logarithmic
C) reciprocal
D) polynomial
E) cubic

Question 13

In testing whether each individual independent variables (Xs)in a multiple regression equation is statistically significant in explaining the dependent variable (Y),one uses the:

A) F-test
B) Durbin-Watson test
C) t-test
D) z-test
E) none of the above

Question 14

In a cross section regression of 48 states,the following linear demand for per-capita cans of soda was found: Cans = 159.17 - 102.56 Price + 1.00 Income + 3.94Temp $$\begin{array} { l r r r } \hline & \text { Coeffcients}& \text { Standard Error } & t \text { Stat } \\\hline \text { Intercept } & 159.17 & 94.16 & 1.69 \\\text {Price } & - 102.56 & 33.25 & - 3.08 \\\text { Income } & 1.00 & 1.77 & 0.57 \\\text { Temperature } & 3.94 & 0.82 & 4.83 \\\hline\end{array}$$
$\mathrm { R } - \mathrm { Sq } = 54.1 \% \quad \mathrm { R } - \mathrm { Sq } ( \mathrm { adj } ) = 51.0 \%$
From the linear regression results in the cans case above, we know that:

A) Price is insignificant
B) Income is significant
C) Temp is significant
D) As price rises for soda,people tend to drink less of it
E) All of the coefficients are significant

Question 15

The estimated slope coefficient (b)of the regression equation (Ln Y = a + b Ln X)measures the ____ change in Y for a one ____ change in X.

A) percentage,unit
B) percentage,percent
C) unit,unit
D) unit,percent
E) none of the above

Question 16

The coefficient of determination measures the proportion of the variation in the independent variable that is "explained" by the regression line.

Question 17

In regression analysis,the existence of a significant pattern in successive values of the error term constitutes:

A) heteroscedasticity
B) autocorrelation
C) multicollinearity
D) nonlinearities
E) a simultaneous equation relationship

Question 18

Using a sample of 100 consumers,a double-log regression model was used to estimate demand for gasoline.Standard errors of the coefficients appear in the parentheses below the coefficients.
$\operatorname { Ln } \mathrm { Q } = 2.45 - 0.67 \operatorname { Ln } \mathrm { P } + .45 \operatorname { Ln } \mathrm { Y } - .34 \operatorname { Ln } \mathrm { P } _ { \text {cars } }$
$\begin{array} { l l l }( .20 ) & ( .10 ) & ( .25 ) \end{array}$

A) Gasoline is inelastic.
B) Gasoline is a normal good.
C) Cars and gasoline appear to be mild complements.
D) The coefficient on the price of cars (P_cars)is insignificant.
E) All of the coefficients are insignificant.

Question 19

Caution must be exercised in using regression models for prediction when:

A) the value of the independent variable lies inside the range of observations from which the model was estimated
B) the value of the independent variable lies outside the range of observations from which the model was estimated
C) diminishing returns are present
D) the existence of saturation levels are present
E) none of the above

Question 20

The presence of association between two variables does not necessarily imply causation for the following reason(s):

A) the association between two variables may result simply from pure chance
B) the association between two variables may be the result of the influence of a third common factor
C) both variables may be the cause and the effect at the same time
D) a and b
E) a,b,and c

Question 21

In which of the following econometric problems do we find Durbin-Watson statistic being far away from 2.0?

A) the identification problem
B) autocorrelation
C) multicollinearity
D) heteroscedasticity
E) agency problems

Question 22

When there is multicollinearity in an estimated regression equation,

A) the coefficients are likely to be small.
B) the t-statistics are likely to be small even though the R² is large.
C) the coefficient of determination is likely to be small.
D) the problem of omitted variables is likely.
E) the error terms will tend to have a cyclical pattern.

Question 23

Even though insignificant explanatory variables can raise the adjusted R² of a demand function,one should not interpret their effects on the regression when

A) testing marketing hypotheses about the determinants of demand
B) analyzing inventory relative to capacity requirements
C) forecasting unit sales for operations planning
D) sales revenue reaches its peak
E) planning for capital budgets

Question 24

When two or more "independent" variables are highly correlated,then we have:

A) the identification problem
B) multicollinearity
C) autocorrelation
D) heteroscedasticity
E) complementary products

Question 25

Given the following demand function:
Q = 2.0 P?^1.33 Y^2.0 A^.50
$$\begin{array} { l l } \text { where } & Q = \text { quantity demanded (thousands of units) } \\& P = \text { price ( } \$ / u n i t ) \\& Y = \text { disposable income per capita (\$ thousands) } \\& A = \text { advertising expenditures ( } \$ \text { thousands) }\end{array}$$ determine the following when P = $2/unit,Y = $8 (a) Frice el asticity of demand
(b) The approximate percentage increase in demand if disposable income percentage increases by $3 \%$ .
(c) The approximate percentage increase in demand if advertising expenditures are increased by 5 percent.

Question 26

Which is NOT true about the coefficient of determination?

A) As you add more variables,the R-square generally rises.
B) As you add more variables,the adjusted R-square can fall.
C) If the R-square is above 50%,the regression is considered significant.
D) The R-square gives the percent of the variation in the dependent variable that is explained by the independent variables.
E) The higher is the R-square,the better is the fit.

Question 27

​In a regression equation,one may measure the accuracy of the estimation by:

A) ​calculating the standard deviation of the errors of prediction
B) ​calculating the standard error of the estimate
C) ​estimating the standard deviation of the errors of prediction
D) ​all of the above
E) a and b only

Question 28

Lenny's,a national restaurant chain,conducted a study of the factors affecting demand (sales).The following variables were defined and measured for a random sample of 30 of its restaurants: $$\begin{array} { l l } \mathrm { Y } & = \text { Annual restaurant sales ( } \$ 000 ) \\\mathrm { X } _ { 1 } & = \text { Disposable personal income (per capita) of residents within } 5 \text { mile radius } \\\mathrm { X } _ { 2 } & = \text { License to sell beer/wine } ( 0 = \text { No, } 1 = \mathrm { Yes } ) \\\mathrm { X } _ { 3 } & = \text { Location (within one-half mile of interstate highway- } 0 = \text { No, } 1 = \text { Yes) } \\\mathrm { X } _ { 4 } & = \text { Population (within } 5 \text { mile radius) } \\\mathrm { X } _ { 5 } & = \text { Number of competing restaurants within } 2 \text { mile radius }\end{array}$$ The data were entered into a computerized regression program and the following results were obtained: $$\begin{array} { l l } \text { MULTIPLE R } & .889 \\\text { R-SQUARE } & .79 \\\text { STD. ERROR OF EST. } & .40\end{array}$$ ANALYSIS OF VARIANCE
$\begin{array}{lrrrr} & \text { DF } & \text { Sum Squares } & \text { Mean Sqr. } & \text { F-Stat } \\\hline \text { Regression } & 5 & 326.13 & 65.226 & 18.17 \\\text { Error } & 24 & 86.17 & 3.590 & \\\text { Total } & 29 & 412.30 & &\end{array}$

$\begin{array}{lccr}\text { Variable } & \text { Coefficient } & \text { Std. Error } & \text { T-Value } \\\text { Constant } & .363 & .196 & 1.852 \\\mathrm{X}-1 & .00275 & .00104 & 2.644 \\\mathrm{X}-2 & 76.65 & 93.70 & .818 \\\mathrm{X}-3 & 164.3 & 235.4 & .698 \\\mathrm{X}-4 & .00331 & .00126 & 2.627 \\\mathrm{X}-5 & 46.2 & 12.1 & -3.818\end{array}$ Questions: (a) Give the regression equation for predicting restaurant sales.
(b) Give an interpretation of each of the estimated regression coefficients.
(c) Which of the independent variables (if any) are statistically significant at the .05 level in
(c) "explaining" restaurant sales?
(d) What proportion of the variation in restaurant sales is "explained" by the regression equation?
(e) Perform an F-test (at the 05 significance level) of the overall explanatory power of the regression model.

Question 29

​In addition to prediction,one purpose of regression analysis is:

A) to measure the overall "fit" of the model to the sample observations
B) ​to test whether the slope parameter β is equal to some particular value
C) ​to test whether the slope parameter β is equal to zero
D) ​b and c
E) ​none of the above

Question 30

The constant or intercept term in a statistical demand study represents the quantity demanded when all independent variables are equal to:

A) 1.0
B) their minimum values
C) their average values
D) 0.0
E) none of the above

Question 31

The following demand function has been estimated for Fantasy pinball machines:
Q_D = 3,500 ? 40P + 17.5P_x + 670U + .0090A + 6,500N where $\quad P =$ monthly rental price of Fantasy pinball machines
$\mathrm { P } _ { \mathrm { X } } =$ monthly rental price of Old Chicago pinball machines (their largest competitor)
$\mathrm { U } =$ current unemployment rate in the 10 largest metropolitan areas
$\mathrm { A } =$ advertising expenditures for Fantasy pinball machines
$\mathrm { N } =$ fraction of the U.S. popul ation between ages 10 and 30 (a) What is the point price elasticity of demand for $F$ antasy pinball machines when $P = \$ 150$ , $\mathrm { P } _ { \mathrm { X } } = \$ 100 , \mathrm { U } = .12 , \mathrm {~A} = \$ 200,000$ and $\mathrm { N } = .35 ?$
(b) What is the point cross elasticity of demand with respect to Old Chicago pinball machines for the values of the independent variables given in part (a)?